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Real Options Valuation Help Topics: Option Pricing Fundamentals The Option to Delay a Project The Option to Expand a Project The Option to Abandon a Project Binomial Option Pricing Game Theory Analysis
Under traditional investment analysis (such as that accomplished by the Investment Valuation model), it is reasonable to accept or reject an investment proposal based on its net present value based on the expected cash flows and discount rates at the time of the analysis. However, such cash flows and discount rates change over time, therefore a proposal that has a negative net present value today may have a positive net present value in the future. The option to Delay a project represents the value gained by waiting to take advantage of any upside volatility in the net present value.
On clicking the 'Start' button in the 'Menu' sheet, a form is displayed for the inputs for the option to Delay a project. These are:
- If similar projects or investments have been undertaken or made in the past the standard deviation of cash flows resulting from these projects can be used as a proxy for the standard deviation in cash flows for the proposed investment.
- Probability analysis can be run on simulations of key inputs, such as revenue and cost drivers, market size and market share, to estimate the standard deviation of the resulting present value. While this type of analysis can be accomplished by using sampling analysis in the Analysis ToolPak add-in shipped with Excel, third-party add-ins can facilitate more sophisticated applications.
- The standard deviation of publicly traded firms in the same business or industry can be used a proxy for the proposed investment. This is the least preferred method due to the likely diversity of activities undertaken in other firms and resulting differences in variance characteristics. Such industry specific volatility data can be obtained from third party market data providers (such as those recommended at the Business-Spreadsheets.com web site) and entered into the Pre-Defined sheet for future use across models and proposals. It should be noted that the Pre-Defined sheet can also be utilized to store standard deviation data from similar projects undertaken in the past as described in the first method.
Upon clicking OK, the resulting valuation of the option to Delay is displayed on the 'ModBS' sheet. The first section shows the inputs from the form that can be altered directly here for sensitivity testing.
The next section displays the Outputs, including the key calculation parameters, overall valuation of the option to delay, and a textual summary of the results. The parameters N(d1) and N(d2) represent the range of probability that the project will become viable before the end of the options life. The detailed formula for actual valuation of the call option can be viewed by Clicking on the Overview button in the top right corner of this section. Based on this valuation and the traditional net present value of the project, the textual summary concludes as to whether the project should or should not be undertaken immediately. This summary can be useful for direct insertion into business case proposals and reports.
The final section displays the Partials of the valuation, which are essentially calculations to test the sensitivity of the options value to changes in input values. These are: